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In fluid dynamics, Sauter mean diameter (SMD, d₃₂ or D[3, 2]) is an average of particle size. It was originally developed by German scientist J. Sauter in the late 1920s. It is defined as the diameter of a sphere that has the same volume/surface area ratio as a particle of interest. Several methods have been devised to obtain a good estimate of the SMD.

SMD is typically defined in terms of the surface diameter, d_s:

$d_s=\sqrt{\frac{A_p}{\pi }}$

and volume diameter, d_v:

$d_v={\left(\frac{6V_p}{\pi }\right)}^{1/3},$

where A_p and V_p are the surface area and volume of the particle, respectively. If d_s and d_v are measured directly by other means without knowledge of A_p or V_p, Sauter diameter for a given particle is

$SD=D[3,2]=d_{32}=\frac{d_v^3}{d_s^2}.$

If the actual surface area, A_p and volume, V_p of the particle are known the equation simplifies further:

$\frac{V_p}{A_p}=\frac{\frac{4}{3}\pi (d_v/2{)}^3}{4\pi (d_s/2{)}^2}=\frac{(d_v/2{)}^3}{3(d_s/2{)}^2}=\frac{d_{32}}{6}$

$d_{32}=6\frac{V_p}{A_p}.$

This is usually taken as the mean of several measurements, to obtain the Sauter mean diameter, SMD: This provides intrinsic data that help determine the particle size for fluid problems.

Applications

The SMD can be defined as the diameter of a drop having the same volume/surface area ratio as the entire spray.

$D_s=\frac{1}{\sum _i\frac{f_i}{d_i}}$

$f_i$ is the scalar variable for the dispersed phase

$d_i$ is the discrete bubble size

SMD is especially important in calculations where the active surface area is important. Such areas include catalysis and applications in fuel combustion.

See also

• Sphericity

References

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